A comparison of solutions of two convolution-type unidirectional wave equations
dc.contributor.author | Erbay, Hüsnü Ata | |
dc.contributor.author | Erbay, Saadet | |
dc.contributor.author | Erkip, A. | |
dc.date.accessioned | 2023-08-12T22:15:05Z | |
dc.date.available | 2023-08-12T22:15:05Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0003-6811 | en_US |
dc.identifier.uri | http://hdl.handle.net/10679/8648 | |
dc.identifier.uri | https://www.tandfonline.com/doi/abs/10.1080/00036811.2022.2118117 | |
dc.description.abstract | In this work, we prove a comparison result for a general class of nonlinear dispersive unidirectional wave equations. The dispersive nature of one-dimensional waves occurs because of a convolution integral in space. For two specific choices of the kernel function, the Benjamin–Bona–Mahony equation and the Rosenau equation that are particularly suitable to model water waves and elastic waves, respectively, are two members of the class. We first prove an energy estimate for the Cauchy problem of the non-local unidirectional wave equation. Then, for the same initial data, we consider two distinct solutions corresponding to two different kernel functions. Our main result is that the difference between the solutions remains small in a suitable Sobolev norm if the two kernel functions have similar dispersive characteristics in the long-wave limit. As a sample case of this comparison result, we provide the approximations of the hyperbolic conservation law. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Taylor and Francis | en_US |
dc.relation.ispartof | Applicable Analysis | |
dc.rights | restrictedAccess | |
dc.title | A comparison of solutions of two convolution-type unidirectional wave equations | en_US |
dc.type | Article | en_US |
dc.peerreviewed | yes | en_US |
dc.publicationstatus | Published | en_US |
dc.contributor.department | Özyeğin University | |
dc.contributor.authorID | (ORCID 0000-0002-5167-609X & YÖK ID 119316) Erbay, Hüsnü Ata | |
dc.contributor.authorID | (ORCID 0000-0002-6080-4591 & YÖK ID 119313) Erbay, Saadet | |
dc.contributor.ozuauthor | Erbay, Hüsnü Ata | |
dc.contributor.ozuauthor | Erbay, Saadet | |
dc.identifier.volume | 102 | |
dc.identifier.issue | 16 | |
dc.identifier.startpage | 4422 | |
dc.identifier.endpage | 4431 | |
dc.identifier.wos | WOS:000847716300001 | |
dc.identifier.doi | 10.1080/00036811.2022.2118117 | en_US |
dc.subject.keywords | 35A35 | en_US |
dc.subject.keywords | 35C20 | en_US |
dc.subject.keywords | 35E15 | en_US |
dc.subject.keywords | 35Q53 | en_US |
dc.subject.keywords | Approximation | en_US |
dc.subject.keywords | Benjamin–Bona–Mahony equation | en_US |
dc.subject.keywords | Long wave limit | en_US |
dc.subject.keywords | Non-local wave equation | en_US |
dc.subject.keywords | Rosenau equation | en_US |
dc.identifier.scopus | SCOPUS:2-s2.0-85137115025 | |
dc.relation.publicationcategory | Article - International Refereed Journal - Institutional Academic Staff |
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